n this question, you will calculate the second moment of area for a 4 ✕ 6 piece of lumber about the x − x and y − y axes, as shown. A rectangle with height h and width w > h is centered on the origin of the x y-coordinate plane. The left and right sides of the rectangle, having height h, are parallel to the vertical y – y axis and the top and bottom sides, having width w, are parallel to the horizontal x – x axis. Visit a hardware store and measure the actual dimensions of a typical 4 ✕ 6 piece of lumber. (Enter your answers in inches.) h = in w = in Calculate the second moment of area about the x − x and y − y axes using the measured dimensions. (Enter your answers in in.4.) Ix – x = ______in4 Iy – y = ________in4

Determine Ix for the triangular region shown.

Problem 1. Three circles are tangent externally. The distance between their centers are 60 m, 73 m, and 85 m. Find the radius of the largest circle. Problem 2. Six congruent circles are arranged in a way that each circle is tangent to at least two other circles. If the radius of each circle is 2 m, find the perimeter of the polygon formed by connecting the centers of each circle. Problem 3 If y varies inversely as z and y = 23 when z = 45,000, find y when z = 54,000. Problem 4 From a window of a building 5.25m above the ground, the angle of elevation of the top of a nearby building is 35.6 degrees and the angle of depression of its base is 28.2 degrees. What is the height of the nearby building? Problem 5 From a point A (Elev. 042.5), the angle of elevation of the top of the tower is 35 degrees, from a point B 325 m nearer angle of elevation of the top of the tower is 55 degrees. What is the elevation of the top of the tower? the tower and 18.65 m below the point A, the

1. Find the components of . 2. A Find the components of T2- (Reminder: cos(a) =) 3. Find the angle between and 2. 4. Find the magnitude of the projection of r2 along/parallel to T = 6m 30° 40° Z 8 60° r₁= r₂ = √2 120° 45⁰ a 0 = Y= 2 = 9 m optional